Venice Marco Polo to Padua late night arrival

After you get your luggage, get a taxi to Venice Mestre station. There is a train to Padua at 47 past midnight.

It looks like you can take a bus to Mestre until 0120 but the last train from Mestre to Padova leaves at 0021. If you don't think you can make the 0021 train from Mestre you might want to look into a private driver or get a hotel for the night in the vicinity of the Airport.

There is a Regionale at 47 past midnight. The one at 21 past is a night train and costs more than twice the 3.50 EUR fare of the Regionale.

Have you contacted your hotel about your late arrival? They may have a recommendation for you.